Lars is balancing equations with his study group. He is unsure about one equation because each member of the study group has a different answer. Which of the following equations is correctly balanced?
[tex]$Ca ( OH )_2+ H _3 PO _4 \rightarrow Ca _3( PO _4)_2+6 H _2 O$[/tex]
[tex]$3 Ca ( OH )_2+2 H _3 PO _4- Ca _3( PO _4)_2+6 H _2 O$[/tex]
[tex]$3 Ca ( OH )_2+2 H _3 PO _4- Ca _3( PO _4)_2+3 H _2 O$[/tex]
[tex]$Ca ( OH )_2+2 H _3 PO _4 \rightarrow Ca _3( PO _4)_2+6 H _2 O$[/tex]
Answer (2)
Balance the number of Calcium (Ca) atoms.
Balance the number of Phosphate ( P O 4 ) groups.
Balance the number of Hydrogen (H) atoms.
Verify the number of Oxygen (O) atoms are balanced. The balanced chemical equation is: 3 C a ( O H ) 2 + 2 H 3 P O 4 → C a 3 ( P O 4 ) 2 + 6 H 2 O
Explanation
Understanding the Problem We are tasked with balancing the chemical equation:
C a ( O H ) 2 + H 3 P O 4 → C a 3 ( P O 4 ) 2 + H 2 O
Balancing chemical equations ensures that the number of atoms for each element is the same on both sides of the equation, adhering to the law of conservation of mass.
Balancing the Equation
Balance the number of Calcium (Ca) atoms. There is 1 Ca atom on the left and 3 on the right, so we need to multiply C a ( O H ) 2 by 3:
3 C a ( O H ) 2 + H 3 P O 4 → C a 3 ( P O 4 ) 2 + H 2 O
Balance the number of Phosphate ( P O 4 ) groups. There is 1 P O 4 group on the left and 2 on the right, so we need to multiply H 3 P O 4 by 2:
3 C a ( O H ) 2 + 2 H 3 P O 4 → C a 3 ( P O 4 ) 2 + H 2 O
Balance the number of Hydrogen (H) atoms. On the left, we have 3 × 2 = 6 H atoms from C a ( O H ) 2 and 2 × 3 = 6 H atoms from H 3 P O 4 , totaling 12 H atoms. On the right, we have 2 H atoms from H 2 O . To balance, we need to multiply H 2 O by 6:
3 C a ( O H ) 2 + 2 H 3 P O 4 → C a 3 ( P O 4 ) 2 + 6 H 2 O
Verify the number of Oxygen (O) atoms are balanced. On the left, we have 3 × 2 = 6 O atoms from C a ( O H ) 2 and 2 × 4 = 8 O atoms from H 3 P O 4 , totaling 14 O atoms. On the right, we have 2 × 4 = 8 O atoms from C a 3 ( P O 4 ) 2 and 6 × 1 = 6 O atoms from H 2 O , totaling 14 O atoms. The oxygen atoms are balanced.
Final Balanced Equation The balanced chemical equation is:
3 C a ( O H ) 2 + 2 H 3 P O 4 → C a 3 ( P O 4 ) 2 + 6 H 2 O
Examples
Balancing chemical equations is crucial in various fields, such as medicine and environmental science. For instance, in wastewater treatment, understanding the stoichiometry of reactions helps determine the precise amounts of chemicals needed to neutralize pollutants. If you're treating acidic wastewater with calcium hydroxide, a balanced equation ensures you add the correct amount of C a ( O H ) 2 to neutralize the acid ( H 3 P O 4 ), preventing under- or over-treatment, which could harm the environment or waste resources. This precise control is vital for effective and safe environmental management.
The correctly balanced equation is 3 C a ( O H ) 2 + 2 H 3 P O 4 → C a 3 ( P O 4 ) 2 + 6 H 2 O . All elements are balanced in this equation according to the law of conservation of mass. Therefore, the answer is the second option provided.
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